Highly Scalable Geodynamic Simulations with HyTeG

High-resolution geodynamic simulations of mantle convection are essential to quantitatively assess the complex physical mechanisms driving the large-scale tectonic processes that shape Earth's surface. Accurately capturing small-scale features such as unstable thermal boundary layers requires global resolution on the order of 1 km. This renders traditional sparse matrix methods impractical due to their prohibitively high memory demands and low arithmetic intensity. Matrix-free methods offer a scalable alternative, enabling the solution of large-scale linear systems efficiently. In this work, we leverage the matrix-free Finite Element framework HyTeG to conduct large-scale geodynamic simulations that incorporate realistic physical models. We validate the framework through a combination of convergence studies of the Finite Element approximations against analytical solutions and through geophysical community benchmarks. The latter include test cases with temperature-dependent and nonlinear rheologies. Our scalability studies demonstrate excellent performance, scaling up to problems with about 100 billion ($10^{11}$) unknowns in the Stokes system.

@article{id3077,
  author = {Ilangovan, Ponsuganth and Kohl, Nils and Mohr, Marcus},
  doi = {10.5194/gmd-19-1455-2026},
  journal = {Geoscientific Model Development},
  language = {en},
  number = {19},
  pages = {1455{\textendash}1472},
  title = {Highly Scalable Geodynamic Simulations with HyTeG},
  year = {2026},
}

%O Journal Article
%A Ilangovan, Ponsuganth
%A Kohl, Nils
%A Mohr, Marcus
%R 10.5194/gmd-19-1455-2026
%J Geoscientific Model Development
%G en
%N 19
%P 1455–1472
%T Highly Scalable Geodynamic Simulations with HyTeG
%D 2026